Answer:
4/15.
Step-by-step explanation:
In probability, there are two types of events: the ones that are not related to each other and the ones that are related to each other. The former types of events are called independent events. In such cases, since the occurrence of one event is not related to and does not affect the other event, therefore, the probabilities of both events can be multiplied if they occur together. It is given that:
P(Q) = 7/15.
P(R) = 4/7.
P(Q and R) = P(Q)*P(R) = 7/15 * 4/7 = 4/15.
Therefore, the probability is 4/15!!!
Transformations were performed on pentagon H as shown in the graph. What types of transformations were performed? Do those transformations result in congruent shapes?
A. Translation and dilation, yes
B. Translation and reflection, no
C. Translation and rotation, yes
D. Translation and dilation, no
PLEASE ANSWER
All books in a store are being discounted by 40%.
Let x represent the regular price of any book in the store. Write an expression that can be used to find the sale price of any book in the store.
Answer:
x(1 - .4)
Step-by-step explanation:
x = regular price.
1 - .4 = .6 = 60%
The sale price is equal to the full price (aka x) minus the discounted price (40% of x = 40/100 times x = .4x)
Therefore sale price = x - .4x or x(1 - .4)
VERY EASY WILL GIVE BRAINLEST THANK YOU AND FRIEND YOU How can the Associative Property be used to mentally fine 48 + 82?
Answer:
You can use teh associative property to split 48 and 82 each into 2 peices
(40+8)(80+2) then you can move the parenthesis around. 40+(8+80)+2
40+(88+2)
40+90=130
On a particular day, the wind added 4 miles per hour to Jaime's rate when she was rowing with the wind and subtracted 4 miles per hour from her rate on her return trip. Jaime found that in the same amount of time she could row 48 miles with the wind, she could go only 24 miles against the wind. What is her normal rowing speed with no wind?
Answer:
12 miles per hour
Step-by-step explanation:
Let her normal rowing speed be x
Also note the formula D = RT, where d is distance, R is rate(speed) and T is time
On windy day, her speed is x + 4
On against wind return, her speed is x - 4
With wind, she can go 48 miles in same amount of time when she goes 24 miles against wind. This can be written as:
48 = (x+4)T
24 = (x-4)T
We can write each equation in terms of T and equate both. So we have:
48/x+4 = T
24/x-4 = T
Thus,
[tex]\frac{48}{x+4}=\frac{24}{x-4}\\48(x-4)=24(x+4)\\48x-192=24x+96\\24x=288\\x=\frac{288}{24}\\x=12[/tex]
Thus, Jaime's normal rowing speed is 12 miles per hour
If a polynomial function f(x) has roots 3 and square root of 7, what must also be a root of f(x)
Answer:
x = - [tex]\sqrt{7}[/tex]
Step-by-step explanation:
Radical roots occur in pairs, that is
x = [tex]\sqrt{7}[/tex] is a root then so is x = - [tex]\sqrt{7}[/tex]
Answer:
-√7 = -2.64
Step-by-step explanation:
The polynomial function has roots. The first root is 3 and the second is √7.
When we have a square root that means that we get two roots from the same number but one is negative and the other is positive. For example, if we have:
√x² = ±x
Because we can have:
(-x)² = x², or
(x)²=x².
So a square root always gives us two answers, one negative and the other positive.
Which equations could be used to solve for the unknown lengths of △ABC? Check all that apply.
sin(45°) = 
sin(45°) = 
9 tan(45°) = AC
(AC)sin(45°) = BC
cos(45°) = 
Answer:
sin(45°)= AC/9
cos(45°)= BC/9
Step-by-step explanation:
This is a right angle triangle:
∠ABC =∠CAB = 45°
Now
AC= CB
AB = 9 units.
We will apply sines:
sine(45°)= AC/AB
We know that AB = 9 units.
So substitute the value of side AB
sin(45°)= AC/9
Now apply cos(45°)
cos(45°)= BC/AB
Again substitute the value of AB:
cos(45°)= BC/9
Thus the answer is
sin(45°)= AC/9
cos(45°)= BC/9 ....
Answer:
A
E
Step-by-step explanation:
which function has a removable discontinuity
x-2/x^2-x-2,
x^2-x+2/x+1,
5x/1-x^2,
2x-1/x
Answer:
[tex]\frac{x-2}{x^2-x-2}[/tex]
Step-by-step explanation:
A removable discontinuity is when there is a hole in your graph. This is usually because one X value has been canceled out. Most of the time, it takes factoring to figure out if there is a removable discontinuity when looking at an equation.
First, look at the numerator [tex]x-2[/tex] . This can't be factored any further. However, [tex]x^2-x-2[/tex] can be factored since it is a trinomial (has three terms) .
For the purposes of this example, you may want to think about it as
[tex]1x^2 -1x-2[/tex]
To factor, multiply the the outside coefficients
1 x -2 = -2
Now take the middle coefficient (-1) and ask yourself what two numbers multiply to make -2, but still add to be -1.
-2 x 1 = -2
-2 + 1 = -1
So in factored form, the equation is
[tex]\frac{x-2}{(x-2)(x+1)}[/tex]
Since you have x-2 on both top and bottom, that can be canceled out. x - 2 would be your removable discontinuity in this situation.
A removable discontinuity can occur in a function if there are common factors in both the numerator and denominator that can be canceled out.
Explanation:A function has a removable discontinuity at a particular point if the function is undefined at that point but can be made continuous by redefining the value at that point. To identify the removable discontinuity, we need to factor both the numerator and denominator of the function. By factoring, we can determine if any common factors exist that can be canceled out, resulting in a removable discontinuity.
Let's consider the given functions:
x-2/x^2-x-2: The denominator can be factored as (x-2)(x+1). We can cancel out the common factor x-2, resulting in a removable discontinuity at x=2.x^2-x+2/x+1: The numerator cannot be factored, so there are no removable discontinuities in this function.5x/1-x^2: The numerator and the denominator have no common factors to cancel out, so there are no removable discontinuities in this function.Learn more about Removable Discontinuity here:https://brainly.com/question/24162698
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e equation 2x + 3y = 36, when y = 6?
Answer:
x=9
Step-by-step explanation:
Since y=18
The new equation is [tex]2x+3*6=36[/tex]
Moving some terms, it stays like the following:
[tex]2x=36-18[/tex]
solving for x, give us that x=9
The best fitting straight line for a data set of X-values plotted against y-values is
called
a. a correlation matrix
b. polynomial expansion
c. varimax rotation
d. a regression equation
Answer:
a. a correlation matrix
Step-by-step explanation:
The best fitting straight line for a data set of X-values plotted against y-values is called a correlation matrix.
Which of the following sequences is an arithmetic sequence?
A. {-10,5,-2.5,1.25,...}
B. {100,20,4,0.8,...}
C. {1,4,16,48,...}
D. {-10,-3.5,3,9.5,...}
Answer:
D
Step-by-step explanation:
For a sequence to be an arithmetic sequence, it must have a common difference. In other words, it must either go down by the same number or up by the same number.
Let's look at the choices:
A. {-10,5,-2.5,1.25,...}
-10 to 5, that went up by 15. It has to keep going up by 15 to be arithmetic. However 5+15 is not -2.5 so it isn't arithmetic.
B. {100,20,4,0.8,...}
100 to 20, that went down by 80. Since 20-80 is not 4, then this sequence is not arithmetic.
C. {1,4,16,48,...}
1 to 4, that went up by 3. 4+3 is not 16 so this is not arithmetic.
D. {-10,-3.5,3,9.5,...}
-10 to -3.5, that went up 6.5.
-3.5+6.5=3
3+6.5=9.5
This is arithmetic. It keeps going up by 6.5.
Simplify the expression 43 + 2(3 − 2).
14
16
66
68
Final answer:
To simplify the expression 43 + 2(3 - 2), first solve inside the parentheses (3 - 2 = 1), then multiply by 2 (2 × 1 = 2), and finally add to 43 to get 45.
Explanation:
The question asks to simplify the expression 43 + 2(3 − 2). To simplify, follow the order of operations, often remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). First, solve the expression within the parentheses, which is 3 − 2 = 1. Next, multiply the result by 2 (2 × 1 = 2). Lastly, add this result to 43 to get the final answer, 43 + 2 = 45. This process demonstrates how to approach and simplify mathematical expressions using proper order of operations.
A ; 1/2. B ; 1/3. C ; 2/3 D ; 4/9
Option B, 1/3
Since pepper topping can be in any size pizza, it remains as a 1/3 probability, since there are three toppings per size.
Vector G is 40.3 m long in a
-35.0° direction. Vector His
63.3 m long in a 270° direction.
Find the magnitude of their
vector sum.
magnitude (m)
Enter
Answer:
Approximately 92.51.
Not sure what the desired rounding is since it isn't listed.
Step-by-step explanation:
So the first vector G is 40.3 m long in a -35 degree direction.
Lat's find the components of G.
[tex]G_x=40.3\cos(-35)=33.0118[/tex].
[tex]G_y=40.3\sin(-35)=-23.1151[/tex].
The second vector H is 63.3 m long in a 270 degree direction.
[tex]H_x=63.3\cos(270)=0[/tex].
[tex]H_y=63.3\sin(270)=-63.3[/tex].
The resultant vector can be found by adding the corresponding components:
[tex]R_x=G_x+H_x=33.0118+0=33.0118[/tex]
[tex]R_y=G_y+H_y=-23.1151+(-63.3)=-86.4151[/tex]
Now we are asked to find the magnitude of [tex](R_x,R_y)[/tex] which is given by the formula [tex]\sqrt{R_x^2+R_y^2}[/tex].
Since [tex](R_x,R_y)=(33.0118,-86.4151)[/tex] then the magnitude is [tex]\sqrt{(33.0118)^2+(-86.4151)^2}=\sqrt{8557.34844}=92.51[/tex].
The magnitude of the sum of vector G (40.3m, -35°) and vector H (63.3m, 270°) is found by breaking each vector into its components, summing these components, and using the Pythagorean theorem. The magnitude of the sum of these vectors is approximately 92.1 m.
Explanation:Given that vector G has a magnitude of 40.3 m and is in a -35.0° direction, and vector H has a magnitude of 63.3 m and is in a 270° direction, the sum of these vectors can be determined. This sum is found by breaking each vector into its component forms, adding the components together, and then using the Pythagorean theorem to find the magnitude of the result.
For vector G: Gx = 40.3m * cos(-35) = 33m and Gy = 40.3m * sin(-35) = -23.14m. For vector H: Hx = 0 (as sin(270) equals 0) and Hy = -63.3m (as sin(270) equals -1). The sum vector S = (Gx+Hx, Gy+Hy) = (33m+0 , -23.14m-63.3m) = (33m, -86.44m). Thus, to find the magnitude of the sum of the vectors, we use the Pythagorean theorem: |S| = sqrt((33m)² + (-86.44m)²) = 92.1 m (rounded to 1 decimal place).
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which shows 3x^2-18x=21 as a perfect square equation? what are the solution(s)?
a. (x-3)^2=0; -3
b. (x-3)^2=16; -1 and 7
c. x^2-6x+9; -3
d. 3x^2-18x-21=0, -1 and 7
Answer:
b
Step-by-step explanation:
Given
3x² - 18x = 21 ( divide all terms by 3 )
x² - 6x = 7
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 3)x + 9 = 7 + 9
(x - 3)² = 16 ( take the square root of both sides )
x - 3 = ± [tex]\sqrt{16}[/tex] = ± 4 ( add 3 to both sides )
x = 3 ± 4, hence
x = 3 - 4 = - 1 and x = 3 + 4 = 7
The correct option is b. [tex]\((x-3)^2=16\); -1 and 7.[/tex]
To solve the given quadratic equation [tex]\(3x^2 - 18x = 21\),[/tex] we first divide the entire equation by 3 to simplify it:
[tex]\[ x^2 - 6x = 7 \]\[ x^2 - 6x + 9 - 9 = 7 \] \[ (x - 3)^2 - 9 = 7 \][/tex]
Now, we isolate the perfect square on one side:
[tex]\[ (x - 3)^2 = 7 + 9 \] \[ (x - 3)^2 = 16 \][/tex]
This is the perfect square equation. To find the solutions, we take the square root of both sides:
[tex]\[ x - 3 = \pm4 \][/tex]
Now, we solve for \(x\) by adding 3 to both sides:
[tex]\[ x = 3 \pm 4 \][/tex]
This gives us two solutions:
[tex]\[ x = 3 + 4 = 7 \] \[ x = 3 - 4 = -1 \][/tex]
Therefore, the solutions to the equation are [tex]\(x = -1\) and \(x = 7\),[/tex] which corresponds to option b. [tex]\((x-3)^2=16\); -1 and 7.[/tex]
which expression gives the distance between points (1,-2) and (2,4)
Answer:
[tex]\sqrt{37}[/tex]
Step-by-step explanation:
Distance formula
[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]
[tex]d = \sqrt {\left( {1 - 2 } \right)^2 + \left( {-2 - 4 } \right)^2 }[/tex]
Simplify
[tex]d = \sqrt {\left( {-1 } \right)^2 + \left( {-6 } \right)^2 }[/tex]
Simplify
[tex]d = \sqrt {\left 1 + \left 36}[/tex]
[tex]d = \sqrt{37}[/tex]
Answer
[tex]d = \sqrt{37}[/tex]
A recipe says it takes 2&1/2 cups of flour to make a batch of cookies. How many cups of flour are needed to make 3&3/4 batches of cookies?
I got 9&3/8, is that correct?
Step-by-step explanation:
Write a proportion:
2½ cups / 1 batch = x cups / 3¾ batches
Cross multiply:
x × 1 = 2½ × 3¾
To multiply the fractions, first write them in improper form:
x = (5/2) × (15/4)
x = 75/8
Now write in proper form:
x = 9⅜
Your answer is correct! Well done!
If you subtract my number from 300, or if you add my number to 220, you will get the same result. What is my number?
Answer:
40
Step-by-step explanation:
Subtracting a number k from 300 looks like this 300-k.
Adding a number k to 220 looks like this 220+k.
They are saying for some number k that we have 300-k and 220+k is the same value.
That is, 300-k=220+k.
This is the equation we are going to solve for your number.
300-k=220+k
Add k on both sides:
300=220+2k
Subtract 220 on both sides;
80=2k
Divide both sides by 2:
40=k
k=40.
So the number is 40.
Check: 300-40=260 while 220+40=260.
Pls help !!!!!!!!!! I need to get this question right
Answer:
B
Step-by-step explanation:
Answer:
He didn't change the direction of the inequality when he divided both sides by -2.
Step-by-step explanation:
Let's go through each step and see.
First step: They distribute and they did so correctly. -4(x+8)=-4x-32.
Second step: They added 2x on both sides.
Third step: They added 32 on both sides.
Fourth step: The divide both sides by -2 correctly but since this is inequality you must flip the sign.
For example 3>2 but if you multiply both sides by -1 or divide both sides by -1 you get -3<-2.
You have to flip the sign whenever you multiply or divide both sides of inequality by negative number.
Suppose your car has h liters of engine oil in the morning. During the day, some oil may have leaked, you may have added more oil, or both. The oil level in the evening is g liters.
Oil added or consumed during the day equals evening oil level minus morning oil level (g - h).
To calculate how much oil was consumed or added during the day, you can use the formula:
Change in oil = g - h
If the value is positive, it means oil was added.
If the value is negative, it means oil was consumed (leaked or used).
For example, if in the morning your car had 5 liters of oil (h = 5) and in the evening it had 7 liters (g = 7):
Change in oil = 7 - 5 = 2 liters
This means 2 liters of oil were added during the day.
n 1917 the cost of a first-class postage stamp was 3¢. In 1974 the cost for a first-class postage stamp was 10¢. What is the percent of increase in the cost of a first-class postage stamp?
Answer:
233.33 %.
Step-by-step explanation:
The increase is 10 - 3 = 7c.
Percentage increase = 100 * 7 / 3.
= 700 / 3
= 233.33 %.
The cost of a first-class postage stamp increased approximately 233.33% from 1917 to 1974.
To calculate the percent increase in the cost of a first-class postage stamp from 1917 to 1974, follow these steps:
Determine the initial price in 1917: 3¢.Determine the final price in 1974: 10¢.Calculate the increase: 10¢ - 3¢ = 7¢.Divide the increase by the initial price: 7¢ / 3¢ ≈ 2.3333.Convert the result into a percentage: 2.3333 × 100 ≈ 233.33%.Thus, the percent increase in the cost of a first-class postage stamp from 1917 to 1974 is approximately 233.33%.
What is 1(y), when y = -5/8
Final answer:
The expression 1(y), when y = -5/8, is calculated by multiplying 1 by -5/8, which simply yields -5/8.
Explanation:
The task is to find the value of the expression 1(y) when y is given as -5/8. The expression 1(y) can be interpreted as simply '1 times y'. Therefore, we need to multiply the number 1 by -5/8 to find the answer.
1(y) = 1 * (-5/8) = -5/8
This is a basic arithmetic operation, specifically multiplication, commonly encountered in mathematics. When we multiply any number by 1, the result is the number itself, which in this case applies to the negative fraction -5/8.
Which of the following sets could be the sides of a right triangle?{2, 3, square root of 13} {5, 5, 2, square root of 10} { 5, 12, 15 }
Answer:
{2, 3, √13}
Step-by-step explanation:
In a right triangle, the sum of the squares of the two shorter sides equals the square of the third side (Pythagoras).
Let's check each set of sides in turn.
A. {2, 3, √13}
2² + 3² = 4 + 9 = 13
(√13)² = 13
This is a right triangle.
B. {5, 5, 2, √10}
This is a quadrilateral (four sides).
C. {5, 12, 15}
5² + 12² = 25 +144 = 169
15² = 225
This is not a right triangle.
Point T is reflected over the y-axis. Determine the coordinates of its image. T (2, 5)
a(2, -5)
b(2, 5)
c(-2, -5)
d(-2, 5)
Answer:
d. (-2, 5)
Step-by-step explanation:
Point T is reflected over the y-axis.
Therefore, the coordinates are (-2, 5).
Answer:
T' is (-2,5)
Step-by-step explanation:
To reflect a point across the y-axis, you will note the following:
1- the sign x-coordinate of the point is flipped while the value remains the same
2- both the sign and the value of the y-coordinate remain the same
We are given that:
point T is (2,5)
Applying the above:
sign of x-coordinate is flipped and value is the same :
x- coordinate of T' is -2
both sign and value of y-coordinate are the same:
y-coordinate of T' is 5
Based on the above:
T' would be (-2,5)
Hope this helps :)
PLZ HELP
Pre-calculus
[tex]\bf \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad a^{log_a x}=x \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \log_6(\sqrt[3]{6})\implies \log_6(6^{\frac{1}{3}})\implies \cfrac{1}{3} \\\\[-0.35em] ~\dotfill\\\\ \log_2(64)\implies \log_2(2^6)\implies 6 \\\\[-0.35em] ~\dotfill\\\\ -3\log_5(25)\implies -3\log_5(5^2)\implies -3(2)\implies -6 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \log_2(\sqrt[4]{8})\implies \log_2(\sqrt[4]{2^3})\implies \log_2(2^{\frac{3}{4}})\implies \cfrac{3}{4} \\\\[-0.35em] ~\dotfill\\\\ \log_3\left( \frac{1}{81} \right)\implies \log_3\left( \frac{1}{3^4} \right)\implies \log_3(3^{-4})\implies -4[/tex]
Answer:
3/4 goes with [tex]\log_2(8^\frac{1}{4})[/tex]
-4 goes with [tex]\log_3(\frac{1}{81})[/tex]
-6 goes with [tex]-3\log_5(25)[/tex]
1/3 goes with [tex]\log_6(6^\frac{1}{3})[/tex]
Step-by-step explanation:
[tex]\log_6(6^\frac{1}{3})=\frac{1}{3}\log_6(6)=\frac{1}{3}\cdot 1=\frac{1}{3}[/tex]
[tex]\log_2(64)=6 \text{ since } 2^6=64[/tex]
[tex]-3\log_5(25)=-3(2)=-6 \text{ since } 5^2=25[/tex]
[tex]\log_2(8^\frac{1}{4})=\frac{1}{4}\log_2(8)=\frac{1}{4}\log_2(2^3)=\frac{1}{4}\cdot (3)\log_2(2)=\frac{1}{4} \cdot 3 \cdot 1=\frac{3}{4} [/tex]
[tex] \log_3(\frac{1}{81})=\log_3(\frac{1}{3^4})=\log_3(3^{-4})=-4\log_3(3)=-4(1)=-4[/tex]
Here are few rules I used:
[tex]\log_a(b)=x \text{ means } a^x=b[/tex]
[tex]\log_a(a)=1 [/tex]
[tex]\log_a(b^r)=r \log_a(b)[/tex]
Which is the equation of a line with a slope
of 1 and a y-intercept of 2?
(1) y + x = 2 (3) y - x + 2 = 0
2) y - x = 2 (4) y + x - 2 = 0
Please help
Answer:
2) y-x=2
Add x on both sides:
y =x+2
The slope is 1 and the y-intercept is 2.
Step-by-step explanation:
So a linear equation in slope-intercept form is y=mx+b where m is the slope and b is the y-intercept.
Let's put all of these in that form:
1) y+x=2
Subtract x on both sides:
y =-x+2
The slope is -1 and the y-intercept is 2.
2) y-x=2
Add x on both sides:
y =x+2
The slope is 1 and the y-intercept is 2.
3) y-x+2=0
Add x on both sides:
y +2=x
Subtract 2 on both sides:
y =x-2
The slope is 1 and the y-intercept is -2.
4) y+x-2=0
Add 2 on both sides:
y +x =2
Subtract x on both sides:
y =-x+2
The slope is -1 and and the y-intercept is 2.
Maria earns $60.00 for 8 hours of work and Marc earns $46.50 for 6 hours of work. Which person earns the most per hour? A. Maria. B. Marc. C. They earn the same amount. D. It cannot be determined.
Answer:
C. Marc
Step-by-step explanation:
to get the amount they earn in an hour divide the amount they earn by the amount of hours they worked for.
Maria: 60 divided by 8 = 7.50
Marc: 46.50 divided by 6 = 7.75
Which of these is the quadratic parent function?
Answer:
C) f(x) = x2
Step-by-step explanation:
he function f(x) = x^2 + 10x - 3 written in vertex form is fx) = (x+5)^2– 28. What are the coordinates of the vertex?
0 (-5, -28)
O (-5, 28)
O (5.-28)
O (5, 28)
Answer:
(- 5, - 28 )
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
f(x) = (x + 5)² - 28 ← is in vertex form
with vertex (h, k) = (- 5, - 28)
What is a counter example for: If the name of the month begins with a J, then it is a summer month.
Answer:
January
Step-by-step explanation:
January is a counter-example of the name of the month begins with a January then it's a winter month by a season.
The counter example is : January since it begins with the letter J and is a winter month, which is not summer.
What is a counter example?An example that disproves a statement (shows that it is false) is called a counter example.
How to find the counter example for the given examples?According to the problem, the given statement is : If the name of the month begins with a J, then it is a summer month.The counter example will be : January since January is a month that starts with J that is not a summer month
January is the only month that fits this criteria.
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Multiply. Express your answer in simplest form. 1/8 × 5/6
5/12
5/48
5/32
3/20
Answer:
5/48
Step-by-step explanation:
1x5=5
8x6=48
which give u
5/48
Answer:
[tex]\large\boxed{\dfrac{5}{48}}[/tex]
Step-by-step explanation:
[tex]\dfrac{1}{8}\times\dfrac{5}{6}=\dfrac{1\times5}{8\times6}=\dfrac{5}{48}\leftarrow\text{this is the simplest form}[/tex]